In this appendix, we solve for the propagation of the shock in two dimensional cartesian coordinates. Unlike spherical coordinates, where both the initial conditions as well as boundary conditions at \(r=0\)  have to be provided, in cartesian coordinates only the initial conditions are required for determining the solution at any time. Thus, numerically solving the equations in cartesian coordinates allows us to determine the boundary conditions at \(r=0\)  for the solution in spherical coordinates. The continuity equations for mass, momentum and energy for a mono-atomic gas are given by [1]}, [2]}, [3]}
\(&&\partial _t\rho + \vec{\nabla }.\rho \vec{u} = 0,  \\&&\partial _t(\rho u_i) + \vec{\nabla }.(\rho \vec{u}(\vec{u}.i)) + \partial _i p = 2(\vec{\nabla }\mu .\vec{\nabla })u_i + 2\mu ((\vec{\nabla }.\vec{\nabla })\vec{u})_i, \\&&\partial _t\Big [\frac{1}{2}\rho u^2 + \rho T\Big ] + \vec{\nabla }.\Big [\Big (\frac{1}{2}\rho u^2 + \rho T + p\Big )\vec{u}\Big ] = 2\vec{\nabla }\mu .(\vec{u}.\vec{\nabla })\vec{u} + 2\mu \vec{\nabla }.[(\vec{u}.\vec{\nabla })\vec{u}] + \vec{\nabla }.[\lambda \vec{\nabla }T].~~~~\) 
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